Structure of solids

Solids are characterized by their definite shape and also their considerable mechanical strength and rigidity. The particles that compose a solid material(with few exceptions), whether ionic, molecular, covalent or metallic, are held in place by strong attractive forces between them.

1. STRUCTURE OF SOLIDS By Prof. A. Balasubramanian Centre for Advanced Studies in Earth Science University of Mysore, India

2. What are solids? Matter exists in three states as solids, liquids and gas. Many times, Liquid and gaseous states are also collectively called fluid state. Different types of matter have different characteristics. They melt and boil at different temperatures. They might be with different colors or have different odors . Some can stretch without breaking, while others shatter easily. These and many such properties help us to distinguish one kind of matter from another. They also help us choose which kind of material to use for a specific purpose.

3. Solids Solids are characterised by their definite shape and also their considerable mechanical strength and rigidity. The particles that compose a solid material(with few exceptions), whether ionic, molecular, covalent or metallic, are held in place by strong attractive forces between them.

4. Solids Solids tend to resist the deformation of their shape due to strong intra molecular forces and absence of the translatory motion of the structural units called atoms, ions, etc. A solid is relatively non compressible, i.e temperature and pressure have only a slight effect on its volume.

5. Solids Solid substances are rigid , possess a definite shape and their volume varies very less with the variance or change in temperature and pressure. Or , solids have a fixed shape , size and volume.

6. Liquids and gases Liquids are slightly compressible and for practical purpose have a definite volume. But liquids don’t have any fixed shape. They take the shape of the container on which the liquid is kept. Gases are readily compressible and can expand infinitely. Hence a substance in gaseous state takes both the shape and volume of it’s container .

7. In almost all cases it is possible to transform a substance in one physical state into another physical states. For example , by the application of Heat , solids can be converted into liquids and liquid can be further transferred info gas if more heat is applied. And just reverse happens on cooling.

8. Characteristics of the Solids A solid is characterized by structural rigidity and resistance to changes of shape or volume. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary water ice) or irregularly (an amorphous solid such as common window glass).  Solid substances are rigid , possess a definite shape and their volume varies very less with the variance or change in temperature and pressure. Or , solids have a fixed shape , size and volume. Liquids are slightly compressible and for practical purpose have a definite volume.

9. Solids The solids are characterized by incompressibility, rigidity and mechanical strength. The molecules, atoms or ions in solids are closely packed. They are held together by strong forces and cannot move about at random. Thus solids have definite volume, shape, slow diffusion, low vapour pressure and possess the unique property of being rigid. Such solids are known as true solids. E.g. NaCl , KCL, Sugar, Ag, Cu, etc.

10. Solids On the other hand the solid which loses its shape on long standing, flows under its own weight and is easily distorted by even mild distortion force is called pseudo solid e. g. glass, pith etc. Some solids such as NaCl , sugar, sulphur etc. have properties not only of rigidity and incompressibility but also of having typical geometrical forms. These solids are called crystalline solids. While discussing about solids, we need to consider the positions of atoms, molecules or ions, which are essentially fixed in space, rather than their motions( which are important for liquids and gases).

11. Classification of Solids: Crystalline solids have regular ordered arrays of components held together by uniform intermolecular forces. The components of amorphous solids are not arranged in regular arrays. o Crystalline solids = atoms show short and long range order o amorphous (non-crystalline )= atoms show short range order only • Crystalline materials = - atoms(ions or molecules) in repeating 3D pattern (called a lattice) • - long-range order; ex.: NaCl ,

12. Crystalline solids Crystalline solids , or crystals, have distinctive internal structures that in turn lead to distinctive flat surfaces, or faces. The faces intersect at angles that are characteristic of the substance. When exposed to x-rays, each structure also produces a distinctive pattern that can be used to identify the material . The characteristic angles do not depend on the size of the crystal; they reflect the regular repeating arrangement of the component atoms, molecules, or ions in space.

13. Amorphous Solids: • example: glasses • not stable state for most pure metals • can be formed by very rapid cooling (106 K/sec) • readily formed from many metal alloys, semiconductors, oxides - especially at low temperatures • generally less dense than crystalline materials • no crystalline defects since no crystal structure • No ordered structure to the particles of the solid • No well defined faces, angles or shapes • Often are mixtures of molecules which do not stack together well, or large flexible molecules • Examples would include glass and rubber

14. Amorphous solids Amorphous solids have two characteristic properties. When cleaved or broken, they produce fragments with irregular, often curved surfaces; and they have poorly defined patterns when exposed to x-rays because their components are not arranged in a regular array. An amorphous, translucent solid is called a glass. Almost any substance can solidify in amorphous form if the liquid phase is cooled rapidly enough .

15. Amorphous solids Some solids, however, are intrinsically amorphous, because either their components cannot fit together well enough to form a stable crystalline lattice or they contain impurities that disrupt the lattice. For example, although the chemical composition and the basic structural units of a quartz crystal and quartz glass are the same—both are SiO 2  and both consist of linked SiO 4   tetrahedra —the arrangements of the atoms in space are not.

16. Classification of Solids based on Bonding: Solids are classified according to what bonds or forces are responsible for holding the material in the solid state. Covalent bonding= Strong Ionic bonding / Metallic bonding Van der Waals bonding= Weak The solid types include: ionic solids, covalent solids, metallic solids, molecular solids(by hydrogen bonding, by dipole-dipole attractions, by London forces)

17. Types of Solids - ionic solids Ionic solids consist of ion (positive and negative) interlaced to form a 3D array of ions. Ionic Solids by definition are solids composed of oppositely charged ions. They consist of positively charged cations and negatively charged anions. When Ionic Solids are dissolved in water the cations and the anions separate, they become free to move about in the water allowing the solution to conduct electrical current.

18. Ionic solids Ionic solids can be composed of simple ions as see in NaCl (sodium chloride). Ionic solids can also be composed of polyatomic ions as seen in ammonium nitrate NH4NO3 Here we see them individually: NH4+ and NO3- Ionic solids have ions at the points of the lattice that characterize the structure of the solids. Examples include: NaCl , CaF2, Na2S (binary ionics ), NaNO3, K2SO4, Mg(ClO4)2 (ternary) plus others.

19. Types of Solids - covalent solids. Covalent Solids are substances with covalent bonds that extend throughout a crystalline solid, and sometimes the entire crystal is held by very strong forces. In a covalent solid the entire solid is held together with covalent bond. Diamond is a typical covalent solid. All the carbon atoms are bonded together with covalent solids. An example of network covalent solids are two allotrops of carbon: diamond, and graphite. Diamonds have each carbon atom bonded to four other atoms in a tetrahedral fashion/network. Many polymers are also covalent solids. Example : polyethylene .

20. Types of solids- metals: The metals are those elements that are on the left of the periodic chart. This includes the lanthanides and actinides at the usually shown at the bottom of the chart. The metal bond explains metal properties: 1 ) metals conduct electricity easily - since the electrons are very mobile. 2 ) metals are ductile, since the binding electrons move easily to accommodate distortion.

21. For the “molecular solids” the forces responsible for the formation of the solid phase (and the liquid) are the weak forces of: hydrogen bonding/ dipole-dipole attractions London forces.

22. Structure of solids: Solids are characterized by an extended three-dimensional arrangement of atoms, ions, or molecules in which the components are generally locked into their positions. The components can be arranged in a regular repeating three-dimensional array (a crystal lattice), which results in a crystalline solid, or more or less randomly to produce an amorphous solid. With few exceptions, the particles that compose a solid material, whether ionic, molecular, covalent, or metallic, are held in place by strong attractive forces between them.

23. Positions of the atoms When we discuss solids, therefore, we consider the positions of the atoms, molecules, or ions, which are essentially fixed in space, rather than their motions (which are more important in liquids and gases).

24. The constituents of a solid can be arranged in two general ways: they can form a regular repeating three-dimensional structure called a crystal lattice, thus producing acrystalline solid, or they can aggregate with no particular order, in which case they form an amorphous solid (from the Greek ámorphos , meaning “shapeless”).

25. Crystalline solids Crystalline solids , or crystals, have distinctive internal structures that in turn lead to distinctive flat surfaces, or faces. The faces intersect at angles that are characteristic of the substance. When exposed to x-rays, each structure also produces a distinctive pattern that can be used to identify the material.

26. The characteristic angles do not depend on the size of the crystal; they reflect the regular repeating arrangement of the component atoms, molecules, or ions in space. When an ionic crystal is cleaved , for example, repulsive interactions cause it to break along fixed planes to produce new faces that intersect at the same angles as those in the original crystal.

27. Levels of Structures in solids Subatomic level = Electronic structure of individual atoms that defines.. interaction among atoms ( interatomic bonding). • Atomic level= Arrangement of atoms in materials (for the same atoms can have different properties, e.g. Steel structures of golf stick) • Microscopic structure= Arrangement of small grains of material that can be identified by microscopy (e.g. brass grains). • Macroscopic structure= Structural elements that may be viewed with the naked eye.

28. The Arrangement of Atoms in Crystalline Solids Because a crystalline solid consists of repeating patterns of its components in three dimensions (a crystal lattice), we can represent the entire crystal by drawing the structure of the smallest identical units that, when stacked together, form the crystal. This basic repeating unit is called a unit cell.

29. Concept of unit cells The concept of unit cells is extended to a three-dimensional lattice. For example, the unit cell of a sheet of identical postage stamps is a single stamp, and the unit cell of a stack of bricks is a single brick. Unit cells are easiest to visualize in two dimensions. Usually the smallest unit cell that completely describes the order is chosen. The only requirement for a valid unit cell is that repeating it in space must produce the regular lattice.

30. The Unit Cell A small volume of a crystal that can be used to reproduce the entire crystal, is called as a Unit cell. But it is not a unique entity. When a unit cell is repeatedly translated to fill all of 2D or 3D space, the vertices of all the unit cells in the filled space constitute a  lattice .

31. Unit cells: Lattice : periodic arrangement of atoms in a crystal. These locations of atoms are called as lattice points. Lattice points are the dots used to represent a particular atomic array, in a crystal. The point can be an atom, a group of atoms, an ion or a molecule. A small volume of a crystal that can be used to reproduce the entire crystal, is called as a Unit cell. But it is not a unique entity. When a unit cell is repeatedly translated to fill all of 2D or 3D space, the vertices of all the unit cells in the filled space constitute a  lattice .

32. A unit cell A unit cell is a small volume of the crystal that can be used to reproduce the entire crystal. A unit cell is not a unique entity. In 3D, non-primitive cells are of three kinds: end- centered  : an extra lattice point is centered in each of two opposing faces of the cell face- centered  : an extra lattice point is centered in every face of the cell body- centered  : an extra lattice point is centered in the exact middle of the cell.

33. Inter -facial angles Similarly, the  inter-facial angles  of the unit cell are defined to be: alpha  : angle between edges  b  and  c beta  : angle between edges  a  and  c gamma  : angle between edges  a  and  b

34. Lattice: Lattice: periodic arrangement of atoms in a crystal. These locations of atoms are called as lattice points. Lattice points are the dots used to represent a particular atomic array, in a crystal. The point can be an atom, a group of atoms, an ion or a molecule.

35. Seven fundamentally different kinds of unit cells There are seven fundamentally different kinds of unit cells, which differ in the relative lengths of the edges and the angles between them. Each unit cell has six sides, and each side is a parallelogram. We focus primarily on the cubic unit cells, in which all sides have the same length and all angles are 90°, but the concepts that we introduce also apply to substances whose unit cells are not cubic.

36. General Features The General Features of the Seven Basic Unit Cells are shown in this figure. The lengths of the edges of the unit cells are indicated by a, b, and c, and the angles are defined as follows: α, the angle between b and c; β, the angle between a and c; and γ, the angle between a and b .

37. Unit cell types

38. Unit cells If the cubic unit cell consists of eight component atoms, molecules, or ions located at the corners of the cube, then it is called simple cubic. If the unit cell also contains an identical component in the center of the cube, then it is body- centered cubic If there are components in the center of each face in addition to those at the corners of the cube, then the unit cell is face- centered cubic ( fcc ) 

39. Three kinds of cubic unit cells For the three kinds of cubic unit cells, simple cubic (a), body- centered cubic ( b), and face- centered cubic (c), there are three representations for each: a ball-and-stick model, a space-filling cutaway model that shows the portion of each atom that lies within the unit cell, and an aggregate of several unit cells.

40. Any intensive property of the bulk material, such as its density, must therefore also be related to its unit cell. Because density is the mass of substance per unit volume, we can calculate the density of the bulk material from the density of a single unit cell. To do this, we need to know the size of the unit cell (to obtain its volume), the molar mass of its components, and the number of components per unit cell.

41. When we count atoms or ions in a unit cell, however, those lying on a face, an edge, or a corner contribute to more than one unit cell. A solid consists of a large number of unit cells arrayed in three dimensions. For example, an atom that lies on a face of a unit cell is shared by two adjacent unit cells and is therefore counted as 12 atom per unit cell.

42. Similarly, an atom that lies on the edge of a unit cell is shared by four adjacent unit cells, so it contributes 14 atom to each. An atom at a corner of a unit cell is shared by all eight adjacent unit cells and therefore contributes 18 atom to each.

43. In contrast, atoms that lie entirely within a unit cell, such as the atom in the center of a body- centered cubic unit cell, belong to only that one unit cell. For all unit cells except hexagonal, atoms on the faces contribute 12 atom to each unit cell, atoms on the edges contribute 14 atom to each unit cell, and atoms on the corners contribute 18 atom to each unit cell.

44. The Arrangement of Atoms in Crystalline Solids Because a crystalline solid consists of repeating patterns of its components in three dimensions (a crystal lattice), we can represent the entire crystal by drawing the structure of the smallest identical units that, when stacked together, form the crystal. This basic repeating unit is called as unit cell. For example, the unit cell of a sheet of identical postage stamps is a single stamp, and the unit cell of a stack of bricks is a single brick. Unit cells are easiest to visualize in two dimensions.

45. A Crystal: A Crystal is a solid composed of atoms, ions, or molecules arranged in a pattern that is repeated in three dimensions. A crystal is a material in which atoms are situated in a repeating or periodic array over large atomic distances.

46. Crystals are composed of Crystals are composed of three-dimensional patterns. These patterns consist of atoms or groups of atoms in ordered and symmetrical arrangements which are repeated at regular intervals keeping the same orientation to one another. By replacing each group of atoms by a representative point a crystal lattice is obtained. 

47. Crystal Lattices: A lattice is a 3-D system of points that enable it to designate the positions of the: atoms, ions, or molecules that make up the substance. Lattice energy is the energy that is lost when separated ions (gaseous), positive or negative, come together and form a solid ionic compound . The lattice energy of an ionic solid is what an ionic solid depends on to dissolve in a solvent.

48. A crystal lattice A crystal lattice is a set of infinite, arranged points related to each other by transitional symmetry. The outlines for such patterns are called lattices. Lattices are comprised of the intersections of three parallel planes. Then lattice sites are occupied by atoms, and of the atoms of the crystal. Thus , the lattice sites are occupied by atoms, and vectors that connect the nearest equivalent atoms. The unit cell contains at least one atom of each of the types that make up the crystal. Providing that the unit cell is made up of only one type of atom, it is called monatomic, anymore than that and it is polyatomic. 

49. BRAVAIS LATTICE The work of Auguste Bravais in the early 19th century revealed that there are only fourteen different lattice structures (often referred to as  Bravais lattices ). These fourteen different structures are derived from seven  crystal systems , which indicate the different shapes a unit cell take and four  types of lattices , which tells how the atoms are arranged within the unit. There are fourteen types of lattices that are called the Bravais lattices.

50. Braggs’ law:

51. A Bravais lattice is a set of all equivalent atoms in a crystal that are able to be brought back into themselves when they are displaced by the length of a unit vector in a direction parallel to a unit vector. Bravais lattices are not always primitive, having one point in the unit cell; other points can be found within the cell. These lattices are classified according to symmetry and space rotations into the seven crystal systems.

52. Seven crystal systems A crystal system is a group of crystal structures that are organized according to their axial system used to describe their lattice. There are seven crystal systems or groups, each of which has a distinct atomic lattice .

53. Crystal axes

54. Crystal systems

55. Seven crystal systems The seven crystal systems are a method of classifying crystals according to their atomic lattice or structure. The atomic lattice is a three dimensional network of atoms that are arranged in a symmetrical pattern. The shape of the lattice determines not only which crystal system the stone belongs to, but all of its physical properties and appearance. In some crystal healing practices the axial symmetry of a crystal is believed to directly influence its metaphysical properties. For example crystals in the Cubic System are believed to be grounding, because the cube is a symbol of the element Earth.

56. CUBIC The cubic crystal system is also known as the isometric system. It is characterized by its complete symmetry. This system contains three crystallographic axes, which are perpendicular to each other, as well as all equal in length. These axes are all at angles 90° to one another . The cubic system contains one lattice point at each of its four corners, and has six faces.

57. Cubic Crystal shapes include: Cube (diamond, fluorite, pyrite) Octahedron (diamond, fluorite, magnetite) Rhombic dodecahedron (garnet, lapis lazuli rarely crystallises) Icosi -tetrahedron (pyrite, sphalerite ) Hexacisochedron (pyrite) Common Cubic Crystals: Diamond, Fluorite, Garnet, Spinel , Gold, Pyrite, Silver

58. TETRAGONAL A tetragonal crystal is a simple cubic shape that is extended along its vertical axis to create a rectangular prism. It consists of a square base and top, as well as three axes. These axes have one perpendicular and two horizontal with angels of 90°. Like the cubic system it is composed of six faces.  

59. Tetragonal Crystal shapes include: Four-sided prisms and pyramids Trapezohedrons Eight-sided and double pyramids Icosi -tetrahedron (pyrite, sphalerite ) Hexacisochedron (pyrite) Common Tetragonal Crystals: Anatase , Apophyllite , Chalcopyrite, Rutile , Scapolite , Scheelite , Wulfenite, Zircon.

60. HEXAGONAL The hexagonal crystal system contains four crystallographic axes. These consist of three equal horizontal axes at120° of each other. It has one vertical axis which is perpendicular to the other three, which maybe shorter or longer than the other three, horizontal axes. It is composed of eight faces.

61. Hexagonal Crystal shapes include: Four-sided prisms and pyramids Twelve-sided pyramids Double pyramids Common Hexagonal Crystals: Apatite, Aquamarine, Beryl, Cancrinite , Emerald, Zincite

62. RHOMBOHEDRAL The rhombohedral is a trigonal system, that has a three-dimensional shape similar to a cube, but it has been inclined to one side making it oblique. It consists of three axes, one vertical and two horizontal all laid perpendicular to one another. These axes are at angles of 90° to one another. The rhobohedral is composed of six faces, although since the faces are not square they are more commonly known as rhombi.

63. Rhombohedral Crystal shapes include: Three-sided prisms or pyramids Rhombohedra Scalenohedra Common Trigonal Crystals: Agate, Amethyst, Calcite, Hematite, Jasper, Quartz , Ruby Sapphire.

64. ORTHORHOMBIC Orthorhombic crystal systems consist of three axes. These axes are mutually perpendicular having all different lengths. Yet, the axes angles are all equidistant laying at 90° to each other. The orthorhombic has six faces.

65. Orthorhombic Crystal shapes include: Pinacoids Rhombic prisms Pyramids Double pyramids Common Orthorhombic Crystals: Alexandrite, Andalusite , Celestite , Chrysoberyl .

66. MONOCLINIC A monoclinic system has three unequal axes. The vertical and forward facing axes are inclined toward each other at an oblique angle, and the horizontal axis is perpendicular to the other two axes, this is known as the ortho axis. These angles are all arranged 90° to each other. A monoclinic system is made up of six faces.

67. Monoclinic Crystal shapes include: Basal pinacoids and prisms with inclined end faces Common Monoclinic Crystals: Gypsum, Moonstone, Muscovite (Mica).

68. TRICLINIC A triclinic system is made up of three unequal crystallographic axes. The axes intersect at oblique angles. These angles are 90° to one another. The triclinic system has six faces. 

69. Crystal Planes and Miller Indices Crystal planes  come from the structures known as  crystal lattices . These lattices are three dimensional patterns that consist of symmetrically organized atoms intersecting three sets of parallel planes. These parallel planes are "crystal planes" and are used to determine the shape and structure of the unit cell and crystal lattice. The planes intersect with each other and make 3D shapes that have six faces. These crystal planes define the crystal structure by making axes visible and are the means by which we can calculate the  Miller Indices .

70. Miller Indices The orientation of a surface or a crystal plane may be defined by considering how any plane intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices, ( hkl ). These are a set of numbers that may be used to identify the plane or surface.  

71. Solid structures of crystals The packing of spheres can describe the solid structures of crystals. In a crystal structure, the centers of atoms, ions, or molecules lie on  the lattice points. Atoms are assumed to be spherical to explain the bonding and structures of metallic crystals. These spherical particles can be packed into different arrangements . In closest packed structures, the arrangement of the spheres are densely packed in order to take up the greatest amount of space possible .

72. X-ray Diffraction   A method called  X-ray Diffraction  is used to determine how the crystal is arranged. X-ray Diffraction consists of a X-ray beam being fired at a solid, and from the diffraction of the beams calculated by  Bragg's Law  the configuration can be determined. The unit cell has a number of shapes, depending on the angles between the cell edges and the relative lengths of the edges. It is the basic building block of a crystal with a special arrangement of atoms. The unit cell of a crystal can be completely specified by three vectors, a, b, c that form the edges of a parallelepiped.

73. Packing of Spheres The packing of spheres can describe the solid structures of crystals. In a crystal structure, the centers of atoms, ions, or molecules lie on  the lattice points. Atoms are assumed to be spherical to explain the bonding and structures of metallic crystals. These spherical particles can be packed into different arrangements . In closest packed structures, the arrangement of the spheres are densely packed in order to take up the greatest amount of space possible.

74. Structures Simple Cubic Structure Body- Centered Cubic Structure Hexagonal Close-Packed and Cubic Close-Packed Structures

75. Diamond

76. Unit cell(Cubic) In the simple-cubic structure only the corners of the cube are occupied with atoms. 

77. Face- centered Cubic The face- centered cubic unit cell is a cube (all sides of the same length and all face perpendicular to each other) with an atom at each corner of the unit cell and an atom situated in the middle of each face of the unit cell. In the case of the face- centered cubic unit cell, the atoms lying along the diagonal of each face are in contact with each other. The density of a solid is the mass of all the atoms in the unit cell divided by the volume of the unit cell.

78. Body- Centered Cubic The body- centered cubic unit cell is a more efficient way to pack spheres together and is much more common among pure elements. Each atom has eight nearest neighbors in the unit cell, and 68% of the volume is occupied by the atoms.

79. The body- centered cubic structure The body- centered cubic structure consists of a single layer of spheres in contact with each other and aligned so that their centers are at the corners of a square; a second layer of spheres occupies the square-shaped “holes” above the spheres in the first layer. The third layer of spheres occupies the square holes formed by the second layer, so that each lies directly above a sphere in the first layer, and so forth. All the alkali metals, barium, radium, and several of the transition metals have body- centered cubic structures

80. Cubic Closest Packed

81. Hexagonal Closest Packed In a hexagonal closest packed structure, the third layer has the same arrangement of spheres as the first layer and covers all the tetrahedral holes. Similar to hexagonal closest packing, the second layer of spheres is placed on to of half of the depressions of the first layer. The third layer is completely different than that first two layers and is stacked in the depressions of the second layer, thus covering all of the octahedral holes.

82. Voids in a close-packing In case of close-packed inorganic compounds, the larger atoms or ions occupy positions approximately corresponding to those of equal spheres in a close- packing while the smaller atoms are distributed among the voids.  Three- dimensional close- packings of spheres have two kinds of voids: triangular void in a close-packed layer has a sphere directly over it. triangular void pointing up in one close-packed layer is covered by a triangular void pointing down in the adjacent layer.

83. Defects in crystals

84. Coordination numbers

85. Faces of crystals

86. Crystal faces – Miller indices

87. Faces and Miller Indices

88. Thank you